Answer
The middle 90% of all waist circumferences is between 70.032 cm and 114.968 cm
Work Step by Step
5% of the waist circumferences are above the middle 90%, while another 5% of the waist circumferences are below the middle 90%.
5% = 0.05
First, let's find a z-score so that the area of the standard normal curve to the left of this z-score is equal to 0.05.
According to the Table V, the z-score which gives the closest value to 0.05 is -1.64.
$z=\frac{X-μ}{σ}$
$-1.64=\frac{X-92.5}{13.7}$
$-1.64\times13.7=X-92.5$
$-22.468=X-92.5$
$X=-22.468+92.5=70.032$
Now, we need to find a z-score so that the area of the standard normal curve to the right of this z-score is equal to 0.05. Due to the symmetry of the standard normal curve, this z-score is $-(-1.64)=1.64$
$z=\frac{X-μ}{σ}$
$1.64=\frac{X-92.5}{13.7}$
$1.64\times13.7=X-92.5$
$22.468=X-92.5$
$X=22.468+92.5=114.968$
